A head-mounted display (hereafter “HMD”) is a device that displays information to a user in a state of being mounted on the head of the user. In terms of mounting on the head, generally it is preferable that the HMD is compact and light, but in terms of display performance, it is preferable that the screen is large and image quality is high. In conventional HMDs, there is a method of optically magnifying an image displayed on a compact crystal panel or the like using a convex lens, a free-form surface prism or the like, so that an expanded fictive image is displayed to the user (e.g. see Patent Document 1). This method of magnifying images with a prism is called an “optical magnification method” in this specification.
In a display device using a computer generated hologram (hereafter “CGH”), a diffraction pattern, which is calculated by a computer using an image to be displayed as input data, is displayed on a phase modulation type liquid crystal panel, and a laser beam is irradiated onto the liquid crystal panel and is diffracted, whereby the wavefront of the display light from the fictive image position is reproduced, and the fictive image is displayed to the user (e.g. see Patent Document 2). The CGH method is characterized in that a three-dimensional stereoscopic image can be displayed at a position near side of or behind the liquid crystal panel. There is also a conventional art that displays a three-dimensional stereoscopic image to a user using a diffraction pattern, although a CGH method is not used (e.g. see Patent Document 3).
However, in the CGH method, a computation cost to generate a diffraction pattern to be displayed on a liquid crystal panel or the like presents a problem. In general, in computing a diffraction pattern, a diffraction pattern is generated from an image to be displayed to the user (hereafter “original image”) using a generation method based on a point filling method or a Fourier transform. FIG. 22 shows this example.
FIG. 22A shows an example of an original image 401, and FIG. 22B shows an example of a diffraction pattern 402 generated from the original image 401. By displaying this diffraction pattern 402 on a phase modulation type liquid crystal panel or the like, the user can visually recognize the original image 401 based on which the diffraction pattern 402 is generated. On generating this diffraction pattern 402, a display with a higher resolution and a wider viewing angle is implemented as the number of pixels of the original image 401 and the number of pixels of the liquid crystal panel increases, but this also increases the computation amount to generate the diffraction pattern 402.
Now an example of a computation method to generate a diffraction pattern using the point filling method will be described. In the case of the point filling method, an original image (object) is regarded as a set of point light sources, and a diffraction pattern is computed from a phase when the light from each point light source overlaps at each point on the liquid crystal panel.
FIG. 23 is a diagram depicting an example of a positional relationship between an original image 501 and a liquid crystal panel 502 that displays a diffraction pattern on generating the diffraction pattern. In order to generate the diffraction pattern to be displayed on the liquid crystal panel 502 using the point filling method, each point (each pixel) on the original image 501 is regarded as a point light source, as described above. If a point i on the original image 501 has an amplitude αi and a phase φi, a complex amplitude of the light generated from this point i, observed at a point u on the liquid crystal panel 502, is given by the following Expression (1).
ri in Expression (1) denotes a distance between the point i and the point u, and ri is computed by the following Expression (2), where the origin is the center of the liquid crystal panel 502, the coordinates of the point i are (xi, yi, zi), and the coordinates of the point u are (ξ, η).
k in Expression (1) denotes a wave number, and is given by k=2π/λ, where λ denotes a wavelength of the light from the point i. As the complex amplitude of the light from the point i is determined at the point u by the computation using Expression (1), the same computation is performed at each point on the original image 501, and the results are added, whereby the value of the complex amplitude at the point u on the liquid crystal panel 502 can be determined. Expression (3) is an expression to indicate a complex amplitude at the point u.
In the point filling method, a diffraction pattern is generated by performing computation of Expression (3) for each point on the liquid crystal panel 502. In this example, a change of a phase due to a reference light or the like is not illustrated to simplify description.
                                          u            i                    ⁡                      (                          ξ              ,              η                        )                          =                                            a              i                                      r              i                                ⁢          exp          ⁢                      {                          -                              j                ⁡                                  (                                                            kr                      i                                        +                                          ϕ                      i                                                        )                                                      }                                              (        1        )                                          r          i                =                                                            (                                  ξ                  -                                      x                    i                                                  )                            2                        +                                          (                                  η                  -                                      y                    i                                                  )                            2                        +                          z              i              2                                                          (        2        )                                          u          ⁡                      (                          ξ              ,              η                        )                          =                              ∑                          i              =              1                        N                    ⁢                                          ⁢                                    u              i                        ⁡                          (                              ξ                ,                η                            )                                                          (        3        )            
As Expression (1) to Expression (3) indicate, when the number of pixels of the original image 501 and the number of pixels of the liquid crystal panel 502 (the number of pixels of the diffraction pattern) increase, the required number of times of computation increases and the computation cost increases. When a method of generating a diffraction pattern by performing an inverse Fourier transform on the original image 501 is used, computation speed becomes faster but the computation cost increases since the number of pixels increases. In a case where the computation capability of a CGH type display device does not satisfy the requirement of the computation cost for generating the diffraction pattern, the quality of the image displayed to the user drops, including a drop in frame rate. Patent Documents 2 and 3 do not consider this point.
Patent Document 1: Japanese Patent Unexamined Publication No. H8-240773
Patent Document 2: Japanese Translation of PCT Application No. 2008-541145
Patent Document 3: Japanese Patent Unexamined Publication No. H6-202575